Remotely actuated programmable self-folding origami strings using magnetic induction heating.

Transforming planar structures into volumetric objects typically requires manual folding processes, akin to origami. However, manual intervention at sub-centimeter scales is impractical. Instead, folding is achieved using volume-changing smart materials that respond to physical or chemical stimuli, be it with direct contact such as hydration, pH, or remotely e.g., light or magnetism. The complexity of small-scale structures often restricts the variety of smart materials used and the number of folding sequences. In this study, we propose a method to sequentially self-fold millimeter scale origami using magnetic induction heating at $150$ kHz and 3.2 mT. Additionally, we introduce a method for designing self-folding overhand knots and predicting the folding sequence using the magneto-thermal model we developed. This methodology is demonstrated to sequentially self-fold by optimizing the surface, placement, and geometry of metal workpieces, and is validated through the self-folding of various structures, including a 380 ${mm}^2$ croissant, a $321$ mm² box, a $447$ mm² bio-mimetic Mimosa pudica leaf, and an overhand knot covering $524$ mm². Our work shows significant potential for miniature self-folding origami robots owing to the novel sequential folding approach and the ability to achieve remote and tetherless self-folding within constrained environments.